German investor morale sharply rose in November, signaling that economists and analysts believe the worst is over for the euro zone's largest economy.

The ZEW index rocketed to 11.5 points in November versus -3.6 points in October – the first time the index had fallen into negative territory since November 2012.

The results were much better than forecast, with analysts polled by Reuters expecting a reading of only 0.5 points.

The Centre for European Economic Research (ZEW) polls 350 economists and analysts on their outlook on the economic future of Germany and the results come as a surprise, particularly after Germany narrowly avoided falling into recession in the third quarter, data showed last week, with the economy expanding 0.1 percent quarter-on-quarter.

There were better growth figures for the euro zone as a whole, however, with gross domestic product (GDP) growing by 0.2 percent on the previous quarter, according to data from the Eurostat, beating a Reuters forecast of a 0.1 percent expansion.

The recent growth figures for the euro area suggested "that the economy is stabilizing," according to ZEW President Clemens Fuest, and had contributed to the [ZEW] indicator's increase."

"However, the economic environment remains fragile, not least due to ongoing geopolitical tensions," Fuest added in the data report.

Despite the weak data, Germany's politicians and analysts appear divided on whether the government needs to rescue its own economy -- let alone that of the euro zone. Germany's deputy finance minister told CNBC that Germany faced a "question of priorities, not of spending more" in order to stimulate growth.

Michael Meister told CNBC on Monday that Germany's budgetary decisions hinged on keeping the budget balanced. "We have tried to balance the budget but we have looked to see if we could make more investments out of the budget -- which reduces money in other positions. So it's a question of priorities, not of spending more," he said.

Finance Minister Wolfgang Schaeuble said in September that Germany would not take on new debt next year for the first time since 1969. The decision has irked euro zone peers who want Germany to increase investment to help revitalize the euro zone economy.

One German politician told CNBC that it was time that the German government started to spend more.

"I think it's time for the German government to wake up and realize that it's important to invest more, both in the private and public sector," Gerhard Schick, a Green Party representative in the Bundestag told CNBC on Monday.

"It's not only true from the European perspective that Germany as a country should do more but it's true from our own perspective," Schick, who is also the Green Party's finance spokesman, added. "The public infrastructure in Germany is not in a good quality and we should do more to repair highways and public buildings, so I think it's important to increase the investment rate."

Amid such comments there is speculation that the European Central Bank (ECB) could announce it is ready to buy euro zone government bonds as it tries to tackle the low growth and disinflationary environment in the region.

Germany is reluctant for the ECB to take on the debt of other euro zone nations, however, and Jens Weidmann, the president of the German Bundesbank has said it would be a "dangerous path" for the ECB to take.

Juergen Stark, a German economist and former executive board member of the ECB, told CNBC that the European central bank should not do anything without Germany's consent.

"In the medium to long term, to decide against the major shareholder of the ECB [Germany] is not a very promising approach," he told CNBC on Monday.

"So I think at a certain point of time the position of the Bundesbank needs to be taken into account. And it's not just the Bundesbank. There seem to be other members of the governing council who are very reluctant to agree to take this important step to go ahead with the purchase of government bonds."

Stark quit the ECB's Governing Council in 2011 over the bank's decision to potentially buy government bonds, which he strongly opposed.